Problem 1 (A Few Random Steps) Consider four molecules, all starting at the origin, which undergo a 1d random walk, each with a 50% chance of going left or right along the x-axis at each time step. A. After 1 time step, what is the probability that 2 particles have gone left and 2 have gone right? Give your answer as a decimal number between 0 and 1 to 3 decimal places. B. After 2 time steps, what is the probability that all of the particles are at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places. C. After 2 time steps, what is the probability that none of the particles are at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places. D. After two time steps, what is the probability that one or more particles are not at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places.